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A277069
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Decimal expansion of the real part of the root of the function x^y = y.
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1
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9, 9, 1, 1, 2, 0, 1, 4, 7, 9, 9, 1, 8, 7, 7, 4, 0, 4, 6, 9, 5, 2, 5, 2, 3, 9, 8, 9, 0, 4, 7, 7, 4, 4, 1, 8, 7, 2, 5, 9, 9, 7, 7, 6, 4, 1, 9, 5, 1, 3, 1, 5, 7, 5, 6, 7, 2, 3, 7, 3, 1, 2, 9, 2, 5, 9, 5, 2, 5, 4, 7, 5, 9, 9, 9, 8, 2, 5, 0, 9, 0, 9, 0, 5, 3, 1, 6, 5
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OFFSET
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2,1
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COMMENTS
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This value is negative.
It is not known if this number has a closed form.
This root occurs on the real component of the function x^y = y for x values which are all real.
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LINKS
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FORMULA
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Original fixed point function is of the form: x^y = y. When solved for y: y = -ProductLog(-log(x))/log(x).
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EXAMPLE
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-99.1120147991877404695252398904774418725997764195131575672373129...
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MATHEMATICA
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FindRoot[Re[-ProductLog[-Log[x]]/Log[x]], {x, -100, -99}, WorkingPrecision -> 261]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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